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Reactor Core Parameters; Artificial Neural Networks as the VVER-1000 Core Predictor

109
No. Title and authors Coupled codes NPP
Transient
type ef.
11
Analysis of a Boron Dilution Accident for
VVER-440
Combining the Use of the Codes DYN3D and
SiTap
U. Rohde, I. Elkin, V. Kalinenko
SiTap
DYN3D
VVER 440 RIA
Grid
frequency
error
injection test
12
RELAP5-PANTHER Coupled
Code Transient Analysis
B.J. Holmes, G.R. Kimber,
J.N. Lillington, M.R. Parkes
RELAP5
PANTHER
PWR
(Sizewell-B)
Single
turbine

Travleev
RELAP5
KAPROS
HPLWR FA tests
16
Analysis and Calculation of an
Accident with Delayed Scram
on NPP Greifswald using the
Coupled Code DYN3D-ATHLET
S. Kliem
ATHLET
DYN3D
VVER-440
(Greifswald)
Delayed
scram
17
Multi-dimensional TMI-1 Main Steam Line
Break Analysis Methodology using TRAC-
PF/NEM
K. Ivanov, T. Beam, A. Baratta, A. Irani, N.
Trikouros
TRAC-PF
NEM
PWR
(B&W TMI-1)
MSLB
18
Realistic and Conservative Rod Ejection
Simulation in a PWR Core at HZP, EOC

The geometry is discretized with a typical mesh size of less than a volume and the thermal-
hydraulics properties are computed for every grid point defined. The conservation equations
for mass momentum and energy are solved in a discrete form. Any complex geometry is
possible, the extremely fine resolution costs computation time. The CFD approach is mostly
preferred for small geometries. Existing CFD codes include: FLUENT, CFX.
4. Coupled neutronic and thermal-hydraulics computer codes for LWR
An overview of available coupled neutronics/thermal-hydraulics code published up to now
has been reported in table 1. This table summarizes a list of coupled codes for PWR, BWR to
date, with the computer codes described in the previous chapters.
4.1 Requirements to the coupling algorithm
Detailed description of the interlace requirement to couple thermal-hydraulics code to 3-D
neutronic code has been reported by Langenbuch et al. The objective to couple neutronics
code with a thermal-hydraulics code is to provide an accurate solution in a reasonable
amount of CPU time. For the present study, the basic components that are considered for
the coupling methodology include:
4.2 Coupling method
There are two different ways of coupling, internal and external coupling. With internal
coupling the neutronics code is integrated within the thermal-hydraulics code. While with
external coupling, the two codes run externally and exchange information between each
other.
4.3 Spatial mesh overlay
Accurate mapping of mesh or volumes between the two codes is important to exchange
information between each other.
4.4 Coupled convergence schemes
A convergence scheme of the two codes needs to be defined. For a final convergence of the
coupled codes, independent convergence in the individual codes is required.
5. Theory of Artificial Neural Network (ANN)
An ANN consists of simple computational units called neurons and it is characterized by a
network structure. The neurons connected to each other with different connection strengths.
The strength of a connection between neurons is called weight. The types of ANNs are

incidence on the prediction parameters are of a crucial importance.
The items of interest are as follow:
1. Activation function,
2. Performance function,
3. Training algorithms.

Fig. 1. Typical architecture of Multi-Layer Perceptron (MLP) neural network

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112
5.2 Cascade feed forward neural networks
A general type of feed-forward ANNs consists of a layer of inputs, a layer of output
neurons, and one or more hidden layers of neurons. Figure 2 shows a general type of a three
layers feed-forward ANN. Typically feed-forward ANNs are used to parameter prediction
and data approximation. Fig. 2. A general type of three layered feed-forward ANNs
A cascade type of feed-forward ANNs consists of a layer of input, a layer of output neurons,
and one or more hidden layers. Similar to a general type of feed-forward ANNs, the first
layer has weights coming from the input. But each subsequent layer has weights coming
from the input and all previous layers. All layers have biases. The last layer is the network
output. Each layer’s weights and biases must be initialized. A supervised training method is
used to train considered cascade feed forward ANNs.
5.3 Training and activation functions
The training process determined through a back propagation algorithm which minimizes a

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113
The output of the neuron O
j
is given by an activation function. An activation derivative
function effects on neuron outputs to compress propagated signals and simulate the
nonlinearity of the complex systems. Many different activation functions are used in feed-
forward ANNs. There are several types of activation functions such as Linear (Eq. (2)), Log-
Sigmoid (Eq. 3), Tan-Sigmoid (Eq. 4) functions, etc.

()
jj
O Pureline V
=
(2)

(
)
()
()1/1
j
V
jj
OLogsigV e
−
==+ (3)

(
)

j
(n) is the desired output; and O
j
(n) is the network output. N and M are the total
number of training data sets and the number of neurons of the output layer. In the gradient
descent method improved values of the weights can be achieved by making incremental
changes Δw
ji
proportional to ∂E
AV
/∂W
ji
(Eq. 6).

A
V
ji
j
i
E
W
W
η
∂
Δ=−
∂
(6)
Where the proportionally factor η is called the learning rate. Large values of η in the
gradient descent formulation may lead to large oscillation or divergence. One attempt to
increase the speed of convergence while minimizing the possibility of oscillation, or

j
is given by:

0.5( ) ( )
kkkk
dOfv
δ
′
=
− (9)

( ) for hidden neurons
jkkkj
k
fv W
δδ
′
=
∑
(10)

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114
It should be noted that the technology of ANNs has been still developing. The determination
of minimum number of necessary hidden neurons and hidden layers is completely practical.
If the hidden neurons are chosen very small, the network will classify its input in a small
number of classes (Wilde, 1997). If the hidden neurons are selected extremely large, the time
of learning process increases ineffectively. Presently, the best method is making an educated
guess. In this work, after primarily studies some practical tests are suggested and used to

1
1
Core parameters
calculator software
1
Neutronic (Keff, Peaking factor, …)
Thermal -Hydraulic(Heat flux ,
DNBR, CHF) parameters
2
2
Validation
Prediction Stage
Learning Stage
2Fig. 3. Overall back-propagation computational strategy for the core parameter prediction
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Reactor Core Parameters; Artificial Neural Networks as the VVER-1000 Core Predictor

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The first stage of computational procedure consists of creating suitable networks by
applying an appropriate learning rule using a desired database. The information required in
the related database will contain coupled input values with the corresponding target output
values. These values are used to train the networks until the error reaches a desired value
stated at the beginning of the learning process. It becomes evident that the quality of the
results obtained will depend on how well knowledge is capitalized in this database. Hence,
significant attention will be focused on how well this database will be created. The main
steps required in the learning process are:
1.

thermal-hydraulics core parameters. During calculation process, MCNP code uses cross
sections library provided by NJOY program. Then calculated fission powers of fuel rods
send to Thermal-hydraulics code for calculating of density and temperature distribution of
fuel and coolant. Finally the results (consist of neutronic and thermal- hydraulic parameters)
are stored on a local data base table. Figure 4 shows the main diagram of creating desired
data.
5.6 Developing of a supporting tool for core parameters calculation
Due of the strong link between the water (moderation) and the neutron spectrum and
subsequently the power distribution, a coupling of neutronics and thermal-hydraulics has Nuclear Power - System Simulations and Operation

116
Data base
tables
Core parameters
calculator software
Outputs
Thermal -
Hydraulic code
Cross -section
Generation code
Neutronic
code
Coupling structure
sending
recieving reading
storing



117
procedure presented will also be applicable to other types of reactors with a density
variation in the core such as in BWR.

NJOY
Neutron Cross
Section
MCNP code
Neutronics analysis
COBRA-EN code
Thermal-hydraulics sub -
channel analysis
Power distribution in the fuel
rods
Fuel, clad and
coolant temperature
distribution
Wate r de ns ity dis tribution
in the s ub-c hannels

Fig. 5. Coupled MCNP/COBRA-EN for joining neutronic –thermalhydraulics are shown
schematically. The cross sections modification are a major concern which are doen using
NJOY code
From the literature review, most of the available coupled codes for neutronics/thermal-
hydraulics are based on diffusion and system codes resulting in a rather coarse resolution of
the core. For a detailed analysis of a VVER-1000 fuel assembly analysis, diffusion codes and
system codes are not giving enough local information. All prior application had been to
PWR and BWR transient analysis. To accurately analyze a VVER fuel assembly a more
detailed analysis fuel rod wise and sub-channel wise is required to predict a hot spot and

core dynamics with recurrent neural networks. Neurocomputing 15 (3–4), 363–
381.
Allaire, G.: Solving Linear System Equation in FLICA, A Thermo-Hydraulic Code for 3-D
Transient Computations, Proc. International Conference on Mathematic and
Computations, Reactor Physics and Environmental Analyses.
Asaka, H., Zimin, V.G., Iguchi, T., Anoda, Y.: Coupling of the Thermal-hydraulics codes
with 3D Neutron Kinetic Code SKETCH-N, Preliminary Proceedings of the
OCED/CSNI Workshop on Advanced Thermal-hydraulics and Neutronics Codes:
Current and Future Applications, Vol.2, pp. 1 — 15, Barcelona, Spain, 2000
Bousbia-Salah, A. et al.: Analysis of the Peach Bottom Turbine Trip 2 Experiment by
Coupled RELAP-PARCS Three-Dimensional Codes, Nuclear Science and
Engineering, Vol. 148, pp337– 353, 2004.
Bovalini, R., D’Auria, F., Galassi, G.M., Spadoni, A., Hassan, Y.: TMI-MSLB Coupled 3-D
Neutronics/Thermal-hydraulics Analysis: Application of RELAP5-3D and
Comparison with Different Codes, RELAP5 International Users Seminar, Sun Vally,
Idaho, 2001.
Briesmeister J.F, Editor, MCNP – A General Monte Carlo N-Transport code, Version 4C, Los
Alamos National Laboratory report LA-12625, 1993.
Broeders, C.H.M., Dagan, R., Sanchez-Espinoza, V, Travleev, A.: KAPROS-E: Modular
Program System for Nuclear Reactor Analysis, Status and Results of Selected
Applications, Jahrrestagung Kerntechnik, Diisseldorf, 2004.
Burwell, M.J.,Lerchl, G., Miro, J., Teschendorff, V., Wolfert, K.: The Thermal-hydraulics
Code ATHLET for Analysis of PWR and BWR Systems, Proceedings Fourth
International Topical Meeting on Nuclear Reactor Thermal-hydraulics, Vol. 2, pp
1234 – 1239, Oct. 10 – 13th,1989.
CFX-4 User Manual,1997, AEA Technology,

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Mathematics and Computation, Reactor Physics and Environmental Analyses.
Grundmann, U., Kliem, S., and Rohde, U.: Analysis of the Boiling Water Reactor Turbine
Trip Benchmark with the Codes DYN3D and ATHLET/DYN3D. Nuclear Science
and Engineering, Vol. 148, Page 226 – 234, 2004.
Hagan, M.T., Demuth, H.B., Beale, M.H., 1995. Neural Network Design. PWS Pub. Co.,
Har/Dsk Edition.
Holland, J.H., 1975. Adaptation in Natural and Artificial Systems. University of Michigan,
Ann Arbor.
Ikonomopoulos, A., Van Der Hagen, T.H.J.J., 1997. A novel signal validation method
applied to a stochastic process. Annals of Nuclear Energy 24 (13), 1057–1067.
Ivanov, K., et al., “Nodal Kinetic Model Upgrade in The Penn State Coupled TRAC/NEM
Codes”, Annl. Nucl. Ener., 26, 1205 (1999).
Ivanov K.N., Juan, R.M., Irani, A., Baratta, A.J.: Features and Performance of a Coupled
Three Dimensional Thermal-hydraulics/kinetics TRAC-PF1/NEM PWR analysis
code, annals of Nuclear Energy 26, 1407 —1417, 1999.

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Jackson, C.J., Finnemann, H.: Verification of the Coupled RELAP/PANBOX System
with the NEACRP LWR Core Transient Benchmark, Proc. International
Conference on Mathematic and Computations, Reactor Physics and
Environmental Analyses
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Joo, H.G., D.A. Barber, G. Jiang and T.J. Downar, PARCS: A Multidimensional Two-group
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Coefficient Calculation for the Super-Critical Water Fast Reactor, Proc. of the
ANS/ENS Topical Meeting GLOBAL, New Orleans, 2003.
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Nigro, A.L., Spadoni, A., D’Auria, F., Saiu, G.: MSLB Coupled 3D Neutronics-Thermal-
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Recent Trends in Mathematical Modeling and
Simulation of Fission Product Transport
From Fuel to Primary Coolant of PWRs
Nasir M. Mirza, Sikander M. Mirza and Muhammad J. Iqbal
Department of Physics and Applied Mathematics,
Pakistan Institute of Engineering and Applied Sciences, Nilore, Islamabad 45650,
Pakistan
1. Introduction
With over 437 operational power plants, nuclear systems contribute 370705 MW(e) worldwide
[1]. The Pressurized Water Reactors (PWR) constitute a two-third majority of the operational
nuclear power plants while the nuclear reactors in planning and construction phases also
show strong trend towards PWRs. These systems are mainly used as baseline load carriers
while conventional fossil fueled systems are used for load adjustments and variations [2].
The PWRs have higher than average levels of radiation fields emanating from the corrosion
and fission product activity [3] [4] [5]. This leads to prolongation of maintenance schedules
entailing loss of revenues mounting to several million dollars per plant annually [6].
Consequently, the plant availability factors are also lowered. This situation is further
aggravated due to strong shift of plant age profile toward over 25 years operational range.
With plant aging, the fuel failures become more frequent which leads to enhancement of
radiation levels in the primary circuits of PWRs.
The levels of fission product activity (FPA) have been of concern both from the operational
as well as from accidental perspectives. These levels are continuously monitored during the
normal operation of PWRs. The fuel pins develop leakages with their burnup. When the
failed fuel fraction exceeds a safe limit, replacement of defective assemblies by refueling
becomes necessary. Therefore, low levels of leaked-out fission products (FPs) in primary
coolant of PWRs are indicative of the core health [7]. In the accidental conditions, the total
value of FPA serves as the available source term that potentially can escape into the
surroundings [8] [9].
The fission products are released in the fuel matrix during burnup. They escape from the
ceramic pellets into the gap between pellets and the clad regions. Hyun et al. [10] have